### v9i1r26 — Comment by authors, Sep 6, 2002 (edited Feb 13, 2012).

After our paper was published, we learned, through James Fill, that the same Markov chain was studied more than two decades ago by Kingman in the context of the "common ancestor problem." The upper bound in Theorem 5 of Kingman [7] is already better than ours, and in the intervening years the result has been generalized and extended. See, for example, Theorem 3 of Donnelly[1], and Möhle[9],[10]. (We gratefully acknowledge Simon Tavaré's help in locating these references.) There is an enormous literature that can be traced back to Kingman's work . We do not attempt a review here, but simply acknowledge our lack of priority.

- P. Donnelly, Weak convergence to a Markov chain with
an entrance boundary: ancestral processes in population genetics,
The Annals of Probability
**19**No.3, (1991) 1102-1117. - P. Donnelly and S. Tavaré, Coalescents and genealogical
structure under neutrality, Annual Review of Genetics
**29**(1995) 401-425. - R.C. Griffiths, Exact sampling distributions from the infinite
neutral alleles model, Advances in Applied Probability
**11**(1979) 326-354. - R.C. Griffiths, Lines of descent in the diffusion approximation
of neutral Wright-Fisher models, Theoretical Population Biology
**17**(1980) 37-50. - J.F.C. Kingman, The Coalescent, Stochastic Proc.
Appl.
**13**(1982) 235-248. - J.F.C. Kingman, On the genealogy of large populations.
Essays in statistical science. J. Appl. Probab.
**19A**(1982) 27-43. - J.F.C. Kingman, Exchangeability and the evolution of large populations, in Exchangeability in probability and statistics, pp. 97-12, North-Holland, Amsterdam-New York, 1982.
- J.F.C. Kingman, Mathematics of genetic diversity.
CBMS-NSF Regional Conference Series in Applied Mathematics
**34**. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1980. - M. Möhle, The time back to the most recent common ancestor in exchangeable population models, Adv. in Appl. Probab. 36(1):78-97, 2004.
- M. Möhle, Total variation distances and rates of convergence
for ancestral coalescent processes in exchangeable population
models, Adv. Appl. Prob.
**32**(2000) 983-993. - S. Tavaré, Line-of-descent and genealogical processes and
their applications in population genetics models, Theoretical
Population Biology
**26**(1984) 119-164. - S. Tavaré , Ancestral inference from DNA Sequence data,
Statistical Science
**4**No.3 (1994) 307-319. - G.A. Watterson, On the number of segregating sites in genetic
models without recombination, Theoretical Population Biology
**7**(1975) 256-276.